Need help getting started!

Hello
Im trying to prove that a function h: R^n -> R^m is differentialbe if and only if each of the m components hi: R^n -> R is differentiable.
I know that i have to use the coordinate projection function and the chain rule for one implication, but im having lots of trouble starting the problem off.
thanks
A.P.

now my proof was that the function is differentiable if and only if each component is differentiable.
and i assumed that one component was not differentable where the entire fn was differentiable. To hopefully find that it is a contradiction.
my work looks like: assume hj is not differentiable

and i went on to say that this is
<= || hi(x) - hi(Xo) - Dhi(x-Xo) + ....+ hj(x) - hj(Xo) - Dhj(x-Xo) +....
but i assumed hj was not differentiable
therefor this is a contradiction, therefor if h is differentiable
then the,
sum (i=1 to m) hi must be differentiable

is this a good proof showing that all components are differentiable.. or am i doing somthing wrong?